A New Numerical Approach for Variable-Order Time-Fractional Modified Subdiffusion Equation via Riemann-Liouville Fractional Derivative

Fractional differential equations describe nature adequately because of the symmetry properties that describe physical and biological processes. In this paper, a new approximation is found for the variable-order (VO) Riemann-Liouville fractional derivative (RLFD) operator; on that basis, an efficient numerical approach is formulated for VO time-fractional modified subdiffusion equations (TFMSDE). Complete theoretical analysis is performed, such as stability by the Fourier series, consistency, and convergence, and the feasibility of the proposed approach is also discussed. A numerical example illustrates that the proposed scheme demonstrates high accuracy, and that the obtained results are more feasible and accurate.